1/5t+1/4t=1

Solution for 1/5t+1/4t=1 equation:

1/5t+1/4t=1

We move all terms to the left:

1/5t+1/4t-(1)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We calculate fractions


4t/20t^2+5t/20t^2-1=0

We multiply all the terms by the denominator


4t+5t-1*20t^2=0

We add all the numbers together, and all the variables

9t-1*20t^2=0

Wy multiply elements

-20t^2+9t=0

a = -20; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-20)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-20}=\frac{-18}{-40}
=9/20
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-20}=\frac{0}{-40}
=0
$